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AP EAPCET 04-Jul-2022 Shift 2 Paper

Section: Mathematics

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Question : 12 of 160

Marks: +1, -0

The sum of the real roots of the equation

|x-2|^{2}+|x-2|-2=0

is

$4$
$-4$
2
$-2$

Solution: 👈: Video Solution

Let

f(x)=|x-2|

\begin{cases} x-2, & x>2 \\ -(x-2), & x<2 \end{cases}

Then, for

x>2

the equation becomes

\;(x-2)^2+(x-2)-2\;=0

\Rightarrow\;x^2-3x\;=0

\Rightarrow\;x\;=0,3

Thus, the root of the equation for

x>2

is 3 . For

x<0

, the equation becomes

\;(x-2)^2+(2-x)-2=0

\Rightarrow\;x^2-5x+4\;=0

\Rightarrow\;(x-4)(x-1)\;=0

\Rightarrow\;x\;=4,1

The root which is less 'than 2 is 1 .

Thus, the roots of given equations are 3,1 .

Sum will be

3+1=4

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